To sense analog signals for processing in digital devices, sampling a signal (significantly) faster than its actual information content changes is a common practice that allows the enhancement of the digitized signal, exploiting the information's redundancy. Examples for such devices include capacitive-touch sensing or touchless position and gesture sensing systems, digital voltmeters, thermometers or pressure sensors.
Exemplary capacitive sensing systems which can be subject to significant noise include the systems described in application note AN1478, “mTouch™ Sensing Solution Acquisition Methods Capacitive Voltage Divider”, and AN1250, “Microchip CTMU for Capacitive Touch Applications”, both available from Microchip Technology Inc., the Assignee of the present application, and hereby incorporated by reference in their entirety.
Another exemplary application is a touchless capacitive 3D gesture system—also known as the GestIC® Technology—manufactured by the Assignee of the present application.
The sensor signals are typically subject to disturbance by various noise types, such as broadband noise, harmonic noise, and peak-noise. The latter two can arise, for example, from switching power supplies, and are also addressed in electro-magnetic immunity standard tests, e.g. IEC 61000-4-4.
The signal acquisition can also be interrupted in a scheduled or deterministic scheme; e.g., when multiplexing several sensors in time, or by irregular events such as data transmission failures. Such discontinuities or missing samples can cause undesired phase jumps in the signal. With digital filters designed for regular sampling intervals, this will corrupt the filter timing and can severely affect their noise-suppression performance.
In analogy to erased messages in the context of channel coding in digital communications (Blahut, 1983; Bossert, 1999) we refer to missing samples and samples that do not carry useful information—e.g., due to peak noise—as Erasures.
FIG. 1a shows a system 100 performing a basic procedure for estimating a noisy, real-valued baseband signal. The Analog-to-Digital Converter (ADC) 110 samples the signal at a rate (significantly) higher than its information changes. The digital signal is then input to a low-pass filter 120 and decimated with rate R by decimator 130. The downsampled result is processed further or is simply displayed, e.g. on a numeric display 140 as shown in FIG. 1a. Therein, the low-pass filter 120 is able to attenuate the higher frequency components of broadband noise, but will not thoroughly suppress noise peaks.
The problem of peak-noise suppression occurs in many applications, such as image processing (T. Benazir, 2013), seismology, and medical (B. Boashash, 2004). A standard approach for fighting peak noise is to apply a Median Filter or variants.
An approach to suppress peak-noise, but still smoothing the input signal, is a filter that averages over a subset of samples in a time window, excluding samples that have been identified as noise peaks or outliers, or excluding, for example, the n largest and the n smallest samples (Selective Arithmetic Mean (SAM) Filter or ‘Sigma Filter’ (Lee, 1983)). Clearly the SAM filter is a time-varying filter with a Finite Impulse Response (FIR) that adapts to the time-domain characteristics of its input signal.
However, while superior in the presence of noise peaks (i.e. with Erasures), without peaks the noise-suppression characteristics of such a SAM averaging filter is inferior to other state-of-the-art filters that, for example, use a Hamming window as impulse response, or filters whose frequency response is designed using the Least Squares method, as shown in FIG. 1b for a window length of 32 samples. In terms of the filters' magnitude responses, the solid curve of the Least-Squares filter and the dashed curve of the Hamming filter show improved side-lobe attenuation, compared to an averaging filter with rectangular impulse response (dash-dotted curve).